Loads

Definition

The load element can be used to model consumption loads (with positive active power) as well as generation loads (with negative active power).

Connections

A load can be either star-connected or delta-connected depending on whether its phases include a neutral or not.

Star (wye) connection

Here is the diagram of a star-connected three-phase load:

European standards

American standards

In Roseau Load Flow, the phases argument of the constructor must contain "n" for star loads.

Note

You can create star connected constant-power or constant-impedance loads even on buses that don’t have a neutral. In this case, the load’s neutral will be floating and its potential can be accessed similar to normal star loads.

Delta connection

Here is the diagram of a delta-connected three-phase load:

European standards

American standards

In Roseau Load Flow, the phases argument of the constructor must not contain "n" for delta loads.

Available Results

The following results are available for all loads:

Result Accessor	Default Unit	Type	Description
res_potentials	\(V\)	complex array	The potentials of each phase of the load
res_currents	\(A\)	complex array	The line currents flowing into each phase of the load
res_powers	\(V\!A\)	complex array	The line powers flowing into each phase of the load
res_voltages	\(V\)	complex array	The phase-to-neutral voltages if the load has a neutral, the phase-to-phase voltages otherwise
res_inner_currents	\(A\)	complex array	The currents flowing in each component (dipole) of the load.
res_inner_powers	\(V\!A\)	complex array	The powers dissipated by each component (dipole) of the load.

Addionally, the following results are available for loads with a neutral:

Result Accessor	Default Unit	Type	Description
res_voltages_pn	\(V\)	complex array	The phase-to-neutral voltages of the load

And the following results are available for loads with more than one phase:

Result Accessor	Default Unit	Type	Description
res_voltages_pp	\(V\)	complex array	The phase-to-phase voltages of the load

And the following results are available for three-phase loads:

Result Accessor	Default Unit	Type	Description
res_voltage_unbalance()	\(\%\)	number	The voltage unbalance of the load according to the IEC definition

Available models

The ZIP model is commonly used to represent electric loads in static grid analysis. This model considers the voltage dependency of loads. ZIP stands for the three load types:

• Z = constant impedance load

• I = constant current load

• P = constant power load

The following load models are available in Roseau Load Flow:

Loads

• Impedance loads (Z)
  • Equations
  • Available Results
  • Usage
• Current loads (I)
  • Equations
  • Available Results
  • Usage
• Power loads (P)
  • Equations
  • Available Results
  • Usage
• Flexible loads
  • Equations
  • Detailed pages
    • Controls
    • Projections
    • Flexible parameters
    • Feasible domains
  • Available Results
  • API Reference

API Reference

class AbstractLoad(id: Id, bus: roseau.load_flow.models.buses.Bus, *, phases: str | None = None, connect_neutral: bool | None = None)

Bases: roseau.load_flow.models.connectables.AbstractConnectable[_CyL_co], abc.ABC

An abstract class of an electric load.

The subclasses of this class can be used to model:

• star-connected loads using a phases constructor argument containing “n”

• delta-connected loads using a phases constructor argument not containing “n”

AbstractLoad constructor.

Parameters:

• id – A unique ID of the load in the network loads.

• bus – The bus to connect the load to.

• phases – The phases of the load. A string like "abc" or "an" etc. The bus phases are used by default. The order of the phases is important. For a full list of supported phases, see the class attribute allowed_phases. All phases of the load must be present in the phases of the connected bus. Multiphase loads are allowed to be connected to buses that don’t have a neutral if connect_neutral is not set to True.

• connect_neutral – Specifies whether the load’s neutral should be connected to the bus’s neutral or left floating. By default, the load’s neutral is connected when the bus has a neutral. If the bus does not have a neutral, the load’s neutral is left floating by default. To override the default behavior, pass an explicit True or False.

element_type: Final = 'load'

The type of the element. It is a string like "load" or "line" etc.

property is_flexible: bool

Whether the load is flexible or not. Only PowerLoad can be flexible.

property res_inner_currents: Q_[ComplexArray]

The load flow result of the currents that flow in the inner components of the load (A).

property res_inner_powers: Q_[ComplexArray]

The load flow result of the powers that flow in the inner components of the load (VA).

Unlike res_powers, the inner powers do not depend on the reference of potentials. They are the physical powers consumed by each of the load dipoles.

classmethod from_dict(data: JsonDict, *, include_results: bool = True) → AbstractLoad

Create an element from a dictionary created with to_dict().

Note

This method does not work on all classes that define it as some of them require additional information to be constructed. It can only be safely used on the ElectricNetwork, LineParameters and TransformerParameters classes.

Parameters:

• data – The dictionary containing the element’s data.

• include_results – If True (default) and the results of the load flow are included in the dictionary, the results are also loaded into the element.

Returns:

The constructed element.

class ImpedanceLoad(id: Id, bus: roseau.load_flow.models.buses.Bus, *, impedances: ComplexScalarOrArrayLike1D, phases: str | None = None, connect_neutral: bool | None = None)

Bases: AbstractLoad[roseau.load_flow_engine.cy_engine.CyAdmittanceLoad | roseau.load_flow_engine.cy_engine.CyDeltaAdmittanceLoad]

A constant impedance load.

ImpedanceLoad constructor.

Parameters:

• id – A unique ID of the load in the network loads.

• bus – The bus to connect the load to.

• impedances –

  A single impedance value or an array-like of impedance values for each phase component. Either complex values (Ohms) or a Quantity of complex values.

  When a scalar value is provided, it creates a balanced load with the same impedance for each phase. To create an unbalanced load, provide a vector of impedance values with the same length as the number of components of the load.

• phases – The phases of the load. A string like "abc" or "an" etc. The bus phases are used by default. The order of the phases is important. For a full list of supported phases, see the class attribute allowed_phases. All phases of the load must be present in the phases of the connected bus. Multiphase loads are allowed to be connected to buses that don’t have a neutral if connect_neutral is not set to True.

• connect_neutral – Specifies whether the load’s neutral should be connected to the bus’s neutral or left floating. By default, the load’s neutral is connected when the bus has a neutral. If the bus does not have a neutral, the load’s neutral is left floating by default. To override the default behavior, pass an explicit True or False.

type: Final = 'impedance'

property impedances: Q_[ComplexArray]

The impedances of the load (Ohms).

class CurrentLoad(id: Id, bus: roseau.load_flow.models.buses.Bus, *, currents: ComplexScalarOrArrayLike1D, phases: str | None = None)

Bases: AbstractLoad[roseau.load_flow_engine.cy_engine.CyCurrentLoad | roseau.load_flow_engine.cy_engine.CyDeltaCurrentLoad]

A constant current load.

CurrentLoad constructor.

Parameters:

• id – A unique ID of the load in the network loads.

• bus – The bus to connect the load to.

• currents –

  A single current value or an array-like of current values for each phase component. Either complex values (A) or a Quantity of complex values. The complex currents provided define the currents magnitudes and their phase shift from the voltages of the load. For example, a current of 10*exp(-90°j) represents an inductive constant current of 10 A.

  When a scalar value is provided, it creates a balanced load with the same current for each phase. To create an unbalanced load, provide a vector of current values with the same length as the number of components of the load.

• phases – The phases of the load. A string like "abc" or "an" etc. The bus phases are used by default. The order of the phases is important. For a full list of supported phases, see the class attribute allowed_phases. All phases of the load must be present in the phases of the connected bus.

type: Final = 'current'

property currents: Q_[ComplexArray]

The currents of the load (Amps).

Setting the currents will update the load’s currents and invalidate the network results.

class PowerLoad(id: Id, bus: roseau.load_flow.models.buses.Bus, *, powers: ComplexScalarOrArrayLike1D, phases: str | None = None, flexible_params: list[roseau.load_flow.models.loads.flexible_parameters.FlexibleParameter] | None = None, connect_neutral: bool | None = None)

Bases: AbstractLoad[roseau.load_flow_engine.cy_engine.CyPowerLoad | roseau.load_flow_engine.cy_engine.CyDeltaPowerLoad | roseau.load_flow_engine.cy_engine.CyFlexibleLoad | roseau.load_flow_engine.cy_engine.CyDeltaFlexibleLoad]

A constant power load.

PowerLoad constructor.

Parameters:

• id – A unique ID of the load in the network loads.

• bus – The bus to connect the load to.

• powers –

  A single power value or an array-like of power values for each phase component. Either complex values (VA) or a Quantity of complex values.

  When a scalar value is provided, it creates a balanced load with the same power for each phase. The scalar value passed is assumed to be the power of each component of the load, not the total multi-phase power. To create an unbalanced load, provide a vector of power values with the same length as the number of components of the load.

• phases – The phases of the load. A string like "abc" or "an" etc. The bus phases are used by default. The order of the phases is important. For a full list of supported phases, see the class attribute allowed_phases. All phases of the load must be present in the phases of the connected bus. Multiphase loads are allowed to be connected to buses that don’t have a neutral if connect_neutral is not set to True.

• flexible_params – A list of FlexibleParameters object, one for each phase. When provided, the load is considered as flexible (or controllable) and the parameters are used to compute the flexible power of the load.

• connect_neutral – Specifies whether the load’s neutral should be connected to the bus’s neutral or left floating. By default, the load’s neutral is connected when the bus has a neutral. If the bus does not have a neutral, the load’s neutral is left floating by default. To override the default behavior, pass an explicit True or False.

type: Final = 'power'

property powers: Q_[ComplexArray]

The powers of the load (VA).

Setting the powers will update the load’s power values and invalidate the network results.

property flexible_params: list[roseau.load_flow.models.loads.flexible_parameters.FlexibleParameter] | None

property is_flexible: bool

property res_flexible_powers: Q_[ComplexArray]

The load flow result of the load flexible powers (VA).

This property is only available for flexible loads.

It returns the “inner powers” of the load instead of the “line powers” flowing into the load connection points. This property is equivalent to the res_inner_powers property, not to the res_powers property. Prefer using res_inner_powers because it is available for all loads.